solve the following inequality
/3x + 12/ >/ 21
PS >/ means greater than or equal to.
I will assume the left side is supposed to be absolute value ...
|3x+12| ≥ 21
3x+12 ≥ 21 OR -3x-12 ≥ 21
3x ≥ 9 or -3x ≥ 33
x≥ 3 or x ≤ -11
To solve the inequality |3x + 12| ≥ 21, we need to consider two cases: when 3x + 12 is positive or zero, and when it is negative.
Case 1: 3x + 12 ≥ 21
Subtracting 12 from both sides:
3x + 12 - 12 ≥ 21 - 12
3x ≥ 9
Dividing both sides by 3:
3x/3 ≥ 9/3
x ≥ 3
Case 2: -(3x + 12) ≥ 21
Multiplying both sides by -1 (which changes the direction of the inequality):
3x + 12 ≤ -21
Subtracting 12 from both sides:
3x + 12 - 12 ≤ -21 - 12
3x ≤ -33
Dividing both sides by 3:
3x/3 ≤ -33/3
x ≤ -11
Therefore, the solution to the inequality |3x + 12| ≥ 21 is x ≥ 3 or x ≤ -11.
To solve the inequality |3x + 12| ≥ 21, you need to consider two cases: when 3x + 12 is positive, and when it is negative. Let's break it down step by step:
Case 1: 3x + 12 ≥ 21
To solve this inequality, you need to isolate x. Begin by subtracting 12 from both sides of the inequality:
3x + 12 - 12 ≥ 21 - 12
3x ≥ 9
Next, divide both sides of the inequality by 3 to solve for x:
3x / 3 ≥ 9 / 3
x ≥ 3
So, for this case, the solution is x ≥ 3.
Case 2: -(3x + 12) ≥ 21
To solve this inequality, you'll first need to distribute the negative sign to both terms inside the absolute value:
-3x - 12 ≥ 21
Next, add 12 to both sides to isolate the variable:
-3x - 12 + 12 ≥ 21 + 12
-3x ≥ 33
Now, divide both sides by -3 (remember that when dividing or multiplying by a negative number, the inequality sign reverses):
-3x / -3 ≤ 33 / -3
x ≤ -11
So, for this case, the solution is x ≤ -11.
To summarize, the solution to the inequality |3x + 12| ≥ 21 is x ≥ 3 or x ≤ -11.